29th International Cosmic Ray Conference Pune (2005) 00, 101–104

Measurement of Chemical Composition Using Telescope ArrayS. Ogio , F. Kakimoto , S. Machida and T. Iguchi ,for Telescope Array Collaboration(a) Graduate School of Science, Osaka City University, Osaka 558-8585, Japan(b) Graduate School of Science and Engineering, Tokyo Institute of Technology, Tokyo 152-8550, Japan

Presenter: H. Tokuno (htokuno@icrr.u-tokyo.ac.jp), jap-tokuno-H-abs3-he15-poster
With observations of air showers by Telescope Array fluorescence detector, we can distinguish primary speciesof cosmic rays with energies greater than  eV event by event. This is mainly because of the good determination accuracies of the longitudinal development of air showers. Assuming cosmic rays consist of threespecies, i.e., protons, carbon nuclei, and iron nuclei, we simulated observed events with TA fluorescence detector and analyzed the data. As a result, we found that we can determine the primary species event by eventwith the accuracy of 60 % using a multivariate analysis technique with the parameters expressing longitudinaldevelopment of air showers, for example, Xmax. When we perform these analysis for actual events, we candetermine the component spectra of cosmic rays, and obtain the correlation between arrival directions and thecomposition. These results are keys to solve the mystery of origins and propagations of cosmic rays.

1.

Introduction

Ultra high energy cosmic rays(UHECRs) are believed to be concerned with the most energetic phenomenain the Universe. Cosmic rays above the ankle are thought to be extragalactic, but the origin of them are not
identified. In order to solve this mystery, we must experimentally obtain many pieces of information, suchas the energy spectrum and the chemical composition. For example, if we find heavier nuclei than protons inUHECRs, this result indicates that UHECRs are accelerated by astronomical objects. Since the characteristics
of source objects and acceleration mechanisms appears on the chemical composition, it is possible to identify
sources with chemical composition studies. On the other hand, Yamamoto et al. pointed out that the major
component of UHECRs transits from light to heavy nuclei with increasing energy owing to the attenuations
and the fragmentations of nuclei during propagations in the inter–galactic space[1]. For this scenario, we needto detailed measurement of the chemical composition to determine whether it is correct or not.
AGASA group reported the detections of doublet and triplet events with high statistical significance[2][3]. This
result indicates the existence of point sources of UHECRs. In order to identify the objects and the acceleration
mechanism, we want to measure the chemical composition of cosmic rays from the point sources. For thesemeasurement we need to distinguish particle species event by event.
With atmospheric fluorescence telescopes used for the Telescope Array(TA) experiment[4] we can observe
longitudinal development profiles of air showers. These are useful information enabling for us to distinguishprimary species. Practically some fluorescence telescope experiment, such as Fly’s Eye[5] and HiRes[6], haveever studied the chemical composition with
 distributions of observed air showers, but they have neverindividually determined particle species. However, since the fluorescence detectors for TA have a high angularresolution, this experiment possesses capability of discriminations of species event by event. In this report, we
propose a method to identify primary species using the multivariate analysis technique. Here, we studied thecapability of the method through Monte Carlo simulations of air shower observations with TA fluorescence
detectors and through the subsequent reconstructions of shower profiles and the multivariate analysis.

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2.

S. Ogio et al.

Telescope Array Fluorescence Detectors

The site of the TA experiment is located at Milard county in Utah, and the altitude is about 1500 m. The TA
fluorescence detector array consists of three telescope stations, each of which contains twelve telescopes of 3.3m diameter. The stations are placed on the edges of the surface detector array, and the separations between
the stations is about 40 km. The field of view of each station has an azimuthal angle of  and a elevation
angles of  . An imaging camera of a telescope has 256 hexagonal PMTs, and the pixel size is nearlycorresponding to  on the celestial sphere. The light falling on a photocathode are converted into an electric
signal, and the signals are recorded as digitized waveforms which are sampled with a frequency of 100 MHz
by FADC electronics. The detailed descriptions of our instruments and techniques will be appeared on othercontribution papers and presentations for this Conference[7].

3.

Simulations

In the simulations we computed longitudinal development profiles of air showers with the Gaisser–Hillas(GH)formula, but we calculated the parameters of this formula and their energy dependences with Monte Carlo simulations of CORSIKA, individually for primary species. Please see the reference[8] for a detailed descriptionsof Monte Carlo simulations and event reconstructions for the TA fluorescence experiment.
Figure 1 and 2 are two dimensional plots of GH formula’s parameters which were obtained with reconstructions
for these events. The plots in Figure 1 are relations between
 and the first interaction depth,   , andthe plots in Figure 2 are relations between
 and the shower size at !"$#&%(' , )+*,-, . In the simulations
weassumed as follows: a) the primary energies are .0/2143657 98:;7  , where the energy fluctuation,<.0/=1>3?;7  is equivalent to the energy determination error with the reconstruction procedure, b) thearrival directions of primary particles are uniformly distributed within zenith angles of less than @; , c) thecore positions are randomly distributed within ACBEDF km, where A+B is an impact parameter of an shower
axis from the center of gravity of the station distributions. We selected events with conditions of, for example,
a track length on imaging cameras, total numbers of detected photo–electrons, a magnitude of G=' of images
fitting to GH formula, and so on. We simulated 15000 events for each primary species, and the remaining
events after the reconstructions and the event selections are 5717 for primary protons, 6126 for carbon nuclei,
and 6466 for iron nuclei. From these figures we can conclude that every parameter considered here depends
on primary species, and then we use these parameters for discriminations of species, as described in the next
section.

Figure 1. Two dimensional distributions of HJI KL and HNMPORQ for reconstructed events which are simulated of primaryprotons(left), carbon nuclei(center), and iron nuclei(right).

Measurement of Chemical Composition Using Telescope Array103

Figure 2. Two dimensional distributions of SJTVUVU and HJMPORQ for reconstructed events which are simulated of primary
protons(left), carbon nuclei(center), and iron nuclei(right).

Table 1. Discriminant Rates and Error Discriminant Rates for Two Component Simulations

primary protons
primary irons

4.

protons(%)
81.9
17.0irons(%)
16.0
81.5

others(%)
2.1
1.5

Multiple Classification Analysis

In order to discriminate primary species event by event we use the nearest neighbour method for GH formula
parameter distributions for reconstructed events. In this analysis, we used the data which are plotted in Figure 1and 2 as group data. Moreover, we simulated 7500 events for each species. After we applied the reconstruction
procedures for these data, the number of the remained sample data is 2927 for protons, 3072 for carbon nuclei,
and 3215 for iron nuclei. In the nearest neighbour method, the position of a sample in the explanatory variable
space is the indicator for the discriminations. Thus, in our case, as explanatory variables we use normalized , +  , and )C*,-, with determination accuracies of each parameters.
The results of the discriminations are shown in Figure 3, and 4. The histograms in Figure 3 are the probability distributions when we assumed cosmic rays consist of two components; protons and iron nuclei. The
histograms in Figure 4 are the distributions under an assumption that cosmic rays consist of three components;
protons, carbon and iron nuclei. When we define the threshold of a discriminant rule is 50%, the discriminant
rates and the error discriminant rates are obtained as listed in Table 1 and 2.

Table 2. Discriminant Rates and Error Discriminant Rates for Three Component Simulations

primary protons
primary carbons
primary irons

protons(%)
53.3
19.9
3.8carbons(%)
40.1
62.5
30.8

irons(%)
4.8
16.6
64.0

others(%)
1.8
1.0
1.4

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Figure 3. The histograms of probabilities for the nearest neighbour method; WYXYZ\[]X_^Y`baP[ a , where, []XYZ\c;Xd^e+Xgf . c;X isthe number of events for the type f particle within the unit length radius from a sample event in explanatory variable space.
e+X is the total number of events or the type f particle. The left panel is for primary proton samples and right panel is forprimary iron nuclei samples.

Figure 4. The histograms of probabilities as same as Figure 3, for three components: protons, carbon nuclei and ironnuclei.

5.

Discussion

As a result, we found that we can discriminate species with a discriminant rate of about 80% if cosmic raysconsist of protons and iron nuclei. When cosmic rays consist of three components, discriminant rates are about
60% for every species. For farther development of analysis procedures and improvement of accuracies , wewill try to use other method of discriminant analysis, and to optimize explanatory variables and normalization
factors. Moreover we plan to add observable values with the surface array as members of explanatory variables.

References[1] T. Yamamoto, et al., Astropart. Phys., 20, 405(2004).
[2] M. Takeda, et al., Astrophys. J. 522, 225 (1999).
[3] N. Hayashida, et al., astro-ph/0008102(2000).
[4] M. Fukushima, et al., 29th ICRC, Pune (2005).
[5] J. D. Bird, et al., Phys. Rev. Lett., 71, 3401(1993).
[6] R. U. Abbasi, et al., astro-ph/0407622(2004).
[7] S. Ogio, et al., 29th ICRC, Pune (2005).
[8] The Telescope Array Project, Design Report(2000).